BAGHDAD—Iraqi forces backed by airstrikes from the U.S.-led coalition pounded Fallujah from the ground and air on Monday, marking the start of a bid to retake one of Islamic State’s last major urban strongholds in the country.

Iraq’s army and counterterrorism forces, along with police, tribal fighters and Shiite Muslim militias, joined in the assault on the strategic city in Anbar province, about 40 miles west of the capital.